Solve For \[$ X \$\] In The Following Equation:$\[ 7 + \frac{x}{5} = 10 \\]$\[ X = \\]

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. In this article, we will focus on solving a linear equation involving fractions. The given equation is $7 + \frac{x}{5} = 10$, and our goal is to isolate the variable $x$ and find its value.

Understanding the Equation

The equation $7 + \frac{x}{5} = 10$ is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, $a = \frac{1}{5}$, $b = 7$, and $c = 10$. The equation involves a fraction, which can be challenging to work with. However, with the right steps, we can simplify the equation and solve for $x$.

Isolating the Fraction

To isolate the fraction, we need to get rid of the constant term $7$ on the left-hand side of the equation. We can do this by subtracting $7$ from both sides of the equation. This gives us:

$$\frac{x}{5} = 10 - 7$$

Simplifying the Equation

Now that we have isolated the fraction, we can simplify the right-hand side of the equation. We can subtract $7$ from $10$ to get:

$$\frac{x}{5} = 3$$

Multiplying Both Sides

To get rid of the fraction, we need to multiply both sides of the equation by $5$. This will give us:

$$x = 3 \times 5$$

Solving for $x$

Now that we have multiplied both sides of the equation by $5$, we can simplify the right-hand side to get:

$$x = 15$$

Conclusion

In this article, we solved the equation $7 + \frac{x}{5} = 10$ to find the value of $x$. We started by isolating the fraction, then simplified the equation, and finally multiplied both sides by $5$ to get rid of the fraction. The final answer is $x = 15$.

Tips and Tricks

• When working with fractions, it's essential to isolate the fraction first before simplifying the equation.
• Multiplying both sides of the equation by a constant can help get rid of fractions.
• Make sure to simplify the equation at each step to avoid confusion.

Real-World Applications

Solving equations like $7 + \frac{x}{5} = 10$ has many real-world applications. For example, in finance, we might need to calculate the interest on a loan or investment. In physics, we might need to calculate the distance traveled by an object. In engineering, we might need to calculate the stress on a material. In all these cases, solving equations like $7 + \frac{x}{5} = 10$ is essential.

Common Mistakes

• Failing to isolate the fraction before simplifying the equation.
• Not multiplying both sides of the equation by a constant to get rid of fractions.
• Not simplifying the equation at each step.

Final Answer

The final answer is $x = 15$.

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Introduction

In our previous article, we solved the equation $7 + \frac{x}{5} = 10$ to find the value of $x$. In this article, we will answer some frequently asked questions related to solving equations like $7 + \frac{x}{5} = 10$.

Q&A

Q: What is the first step in solving the equation $7 + \frac{x}{5} = 10$?

A: The first step in solving the equation $7 + \frac{x}{5} = 10$ is to isolate the fraction. We can do this by subtracting $7$ from both sides of the equation.

Q: How do I simplify the equation after isolating the fraction?

A: After isolating the fraction, we can simplify the equation by subtracting $7$ from $10$ to get $\frac{x}{5} = 3$.

Q: Why do I need to multiply both sides of the equation by $5$?

A: We need to multiply both sides of the equation by $5$ to get rid of the fraction. This will give us $x = 3 \times 5$.

Q: What is the final answer to the equation $7 + \frac{x}{5} = 10$?

A: The final answer to the equation $7 + \frac{x}{5} = 10$ is $x = 15$.

Q: Can I use a calculator to solve the equation $7 + \frac{x}{5} = 10$?

A: Yes, you can use a calculator to solve the equation $7 + \frac{x}{5} = 10$. However, it's essential to understand the steps involved in solving the equation to ensure accuracy.

Q: How do I check my answer?

A: To check your answer, you can plug the value of $x$ back into the original equation and see if it's true. In this case, we can plug $x = 15$ back into the equation $7 + \frac{x}{5} = 10$ to get $7 + \frac{15}{5} = 10$, which simplifies to $7 + 3 = 10$, and finally $10 = 10$. This confirms that our answer is correct.

Q: What if I get a different answer?

A: If you get a different answer, it's essential to recheck your work and ensure that you've followed the correct steps. You can also try plugging your answer back into the original equation to see if it's true.

Tips and Tricks

• Always isolate the fraction before simplifying the equation.
• Make sure to multiply both sides of the equation by a constant to get rid of fractions.
• Check your answer by plugging it back into the original equation.

Common Mistakes

• Failing to isolate the fraction before simplifying the equation.
• Not multiplying both sides of the equation by a constant to get rid of fractions.
• Not checking the answer by plugging it back into the original equation.

Real-World Applications

Solving equations like $7 + \frac{x}{5} = 10$ has many real-world applications. For example, in finance, we might need to calculate the interest on a loan or investment. In physics, we might need to calculate the distance traveled by an object. In engineering, we might need to calculate the stress on a material. In all these cases, solving equations like $7 + \frac{x}{5} = 10$ is essential.

Conclusion

In this article, we answered some frequently asked questions related to solving equations like $7 + \frac{x}{5} = 10$. We covered topics such as isolating the fraction, simplifying the equation, and checking the answer. We also provided tips and tricks for solving equations like $7 + \frac{x}{5} = 10$.